Multiplying Complex Numbers: (−4+2i)⋅(4−4i)
This article explores the process of multiplying two complex numbers: (−4+2i)⋅(4−4i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of 1 (i² = 1).
Multiplication Process
To multiply complex numbers, we follow the distributive property, similar to multiplying binomials:

Expand the product: (−4+2i)⋅(4−4i) = (−4)(4) + (−4)(4i) + (2i)(4) + (2i)(4i)

Simplify: = 16 + 16i + 8i  8i²

Substitute i² with 1: = 16 + 16i + 8i + 8

Combine real and imaginary terms: = (16 + 8) + (16 + 8)i

Final result: = 8 + 24i
Conclusion
Therefore, the product of (−4+2i) and (4−4i) is 8 + 24i. This process demonstrates how complex numbers can be multiplied using the distributive property and the fundamental property of the imaginary unit, i² = 1.